Simulations and Experiments of Stochastic Characteristics for Collective Short Fatigue Cracks in Steels

Stochastic characteristics prevail in the process of short fatigue crack progression. This paper presents a method taking into account the balance of crack number density to describe the stochastic behaviour of short crack collective evolution. The results from the simulation illustrate the stochastic development of short cracks. The experiments on two types of steels show the random distribution for collective short cracks with the number of cracks and the maximum crack length as a function of different locations on specimen surface. The experiments also give the variation of total number of short cracks with fatigue cycles. The test results are consistent with numerical simulations.

Optimal bounded control of first-passage failure of quasi-integrable Hamiltonian systems with wide-band random excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged It$\ddot{\rm o}$ equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.

Stochastic Structural Model of Rock and Soil Aggregates by Continuum-Based Discrete Element Method

This paper first presents a stochastic structural model to describe the random geometrical features of rock and soil aggregates. The stochastic structural model uses mixture ratio, rock size and rock shape to construct the microstructures of aggregates,and introduces two types of structural elements (block element and jointed element) and three types of material elements (rock element, soil element, and weaker jointed element)for this microstructure. Then, continuum-based discrete element method is used to study the deformation and failure mechanism of rock and soil aggregate through a series of loading tests. It is found that the stress-strain curve of rock and soil aggregates is nonlinear, and the failure is usually initialized from weaker jointed elements. Finally, some factors such as mixture ratio, rock size and rock shape are studied in detail. The numerical results are in good agreement with in situ test. Therefore, current model is effective for simulating the mechanical behaviors of rock and soil aggregates.

First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems

An n degree-of-freedom Hamiltonian system with r (1¡r¡n) independent 0rst integrals which are in involution is calledpartially integrable Hamiltonian system. A partially integrable Hamiltonian system subject to light dampings andweak stochastic excitations is called quasi-partially integrable Hamiltonian system. In the present paper, the procedures for studying the 0rst-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems are proposed. First, the stochastic averaging methodfor quasi-partially integrable Hamiltonian systems is brie4y reviewed. Then, basedon the averagedIt ˆo equations, a backwardKolmogorov equation governing the conditional reliability function, a set of generalized Pontryagin equations governing the conditional moments of 0rst-passage time and their boundary and initial conditions are established. After that, the dynamical programming equations and their associated boundary and 0nal time conditions for the control problems of maximization of reliability andof maximization of mean 0rst-passage time are formulated. The relationship between the backwardKolmogorov equation andthe dynamical programming equation for reliability maximization, andthat between the Pontryagin equation andthe dynamical programming equation for maximization of mean 0rst-passage time are discussed. Finally, an example is worked out to illustrate the proposed procedures and the e9ectiveness of feedback control in reducing 0rst-passage failure.

Influence of stochastic mesoscopic structure on macroscopic mechanical behavior of brittle material

A newly developed numerical code, MFPA(2D) (Material Failure Process Analysis), is applied to study the influence of stochastic mesoscopic structure on macroscopic mechanical behavior of rock-like materials. A set of uniaxial compression tests has been numerically studied with numerical specimens containing pre-existing crack-like flaw. The numerical results reveal the influence of random mesoscopic structure on failure process of brittle material, which indicates that the variation of failure mode is strongly sensitive to the local disorder feature of the specimen. And the patterns of the crack evolution in the specimens are very different from each other due to the random mesoscopic structure in material. The results give a good explanation for various kinds of fracture modes and peak strength variation observed in laboratory studies with specimens made from the same rock block being statistically homogenous in macro scale. In addition, the evolution of crack is more complicated in heterogeneous cases than in homogeneous cases.

Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

A theoretical analysis on stochastic behaviour of short cracks and fatigue damage of metals

In this paper, the closed form of solution to the stochastic differential equation for a fatigue crack evolution system is derived. and the relationship between metal fatigue damage and crack stochastic behaviour is investigated. It is found that the damage extent of metals is independent of crack stochastic behaviour ii the stochastic deviation of the crack growth rate is directly proportional to its mean value. The evolution of stochastic deviation of metal fatigue damage in the stage close to the transition point between short and long crack regimes is also discussed.

Optimal bounded control of first-passage failure of strongly non-linear oscillators under combined harmonic and white-noise excitations

A procedure for designing the optimal bounded control of strongly non-linear oscillators under combined harmonic and white-noise excitations for minimizing their first-passage failure is proposed. First, a stochastic averaging method for strongly non-linear oscillators under combined harmonic and white-noise excitations using generalized harmonic functions is introduced. Then, the dynamical programming equations and their boundary and final time conditions for the control problems of maximizing reliability and of maximizing mean first-passage time are formulated from the averaged Ito equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraint. Finally, the conditional reliability function, the conditional probability density and mean of the first-passage time of the optimally controlled system are obtained from solving the backward Kolmogorov equation and Pontryagin equation. An example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation. (C) 2003 Elsevier Ltd. All rights reserved.

A stochastic jump and deterministic dynamics model of impact failure evolution with rate effect

Motivated by the observation of the rate effect on material failure, a model of nonlinear and nonlocal evolution is developed, that includes both stochastic and dynamic effects. In phase space a transitional region prevails, which distinguishes the failure behavior from a globally stable one to that of catastrophic. Several probability functions are found to characterize the distinctive features of evolution due to different degrees of nucleation, growth and coalescence rates. The results may provide a better understanding of material failure.

Effects of stochastic extension in ideal microcrack system

The effects of stochastic extension on the statistical evolution of the ideal microcrack system are discussed. First, a general theoretical formulation and an expression for the transition probability of extension process are presented, then the features of evolution in stochastic model are demonstrated by several numerical results and compared with that in deterministic model.

Anisotropic-source-induced changes of the degree of polarization of stochastic electromagnetic beams on propagation

It is shown that stochastic electromagnetic beams may have different degrees of polarization on propagation, even though they have the same coherence properties in the source plane. This fact is due to a possible difference in the anisotropy of the field in the source plane. The result is illustrated by some examples.

Exploring consensus mRNA secondary (folding) structure units by stochastic sampling and folding simulation

It is extremely difficult to explore mRNA folding structure by biological experiments. In this report, we use stochastic sampling and folding simulation to test the existence of the stable secondary structural units of-mRNA, look for the folding units, and explore the probabilistic stabilization of the units. Using this method, We made simulations for all possible local optimum secondary structures of a single strand mRNA within a certain range, and searched for the common parts of the secondary structures. The consensus secondary structure units (CSSUs) extracted from the above method are mainly hairpins, with a few single strands. These CSSUs suggest that the mRNA folding units could be relatively stable and could perform specific biological function. The significance of these observations for the mRNA folding problem in general is also discussed. (c) 2004 Elsevier B.V. All rights reserved.

Stochastic resonance for modulated gain in a single-mode laser

Stochastic resonance (SR) induced by the signal modulation is investigated, by introducing the signal-modulated gain into a single-mode laser system. Using the linear approximation method, we detailedly calculate the signal-to-noise ratio (SNR) of a gain-noise model of the single-mode laser, taking the cross-correlation between the quantum noise and pump noise into account. We find that, SR appears in the dependence of the SNR on the intensities of the quantum and the pump noises when the correlation coefficient between both the noises is negative; moreover, when the cross-correlation between the two noises is strongly negative, SR exhibits a resonance and a suppression versus the gain coefficient, meanwhile, the single-peaked SR and multi-peaked SR occur in the behaviors of the SNR as functions of the loss coefficient and the deterministic steady-state intensity. (c) 2005 Elsevier B.V. All rights reserved.

Stochastic resonance in single-mode semiconductor lasers

Owing to the considerable virtues of semiconductor lasers for applications, they have become the main optical source for fiber communication systems recently. The behavior of stochastic resonance (SR) in direct-modulated semiconductor laser systems is investigated in this article. Considering the carrier and photon noises and the cross-correlation between the two noises, the power spectrum of the photon density and the signal-to-noise ratio (SNR) of the modulated laser system were calculated using the linear approximation method. We found that the SR always appears in the dependence of the SNR upon the bias current density, and is strongly affected by the cross-correlation coefficient of the carrier and photon noises, the frequency of modulation signal and the photon lifetime in the laser cavity. Hence, it is promising to use the SR mechanism to enhance the SNR of direct-modulated semiconductor laser systems and improve the quality of optical communication. (c) 2006 Elsevier B.V. All rights reserved.

Stochastic resonance in quantum-well semiconductor lasers

The quantum well (QW) semiconductor lasers have become main optical sources for optical fibre communication systems because of their higher modulation speed, broader modulation bandwidth and better temperature characteristics. In order to improve the quality of direct-modulation by means of the stochastic resonance (SR) mechanism in QW semiconductor lasers, we investigate the behaviour of the SR in direct-modulated QW semiconductor laser systems. Considering the cross-correlated carrier noise and photon noise, we calculate the power spectrum of the photon density and the signal-to-noise ratio (SNR) of the direct-modulated laser system by using the linear approximation method. The results indicate that the SR always appears in the dependence of the SNR on the bias current density, and is strongly affected by the cross-correlation coefficient of the carrier and photon noises, the frequency of modulation signal, and the photon lifetime in the laser cavity.